FROMWMAPTOPLANCK: EXACT RECONSTRUCTION OF FOUR- AND FIVE-DIMENSIONAL INFLATIONARY POTENTIAL FROM HIGH-PRECISION COSMIC MICROWAVE BACKGROUND MEASUREMENTS

Abstract

We make a more general determination of the inflationary observables in the standard four-dimensional (4D) and five-dimensional (5D) single-field inflationary scenarios by the exact reconstruction of the dynamics of the inflation potential during the observable inflation with a minimal number of assumptions: the computation does not assume the slow-roll approximation and is valid in all regimes if the field is monotonically rolling down its potential. We address higher order effects in the standard and braneworld single-field inflation scenarios by fitting the Hubbble expansion rate and subsequently the inflationary potential directly to WMAP5+SN+BAO and Planck-like simulated data sets. Making use of the Hamilton-Jacobi formalism developed for the 5D single-field inflation model, we compute the scale dependence of the amplitudes of the scalar and tensor perturbations by integrating the exact mode equation. The solutions in 4D and 5D inflation scenarios differ through the dynamics of the background scalar field and the number of e-folds assumed to be compatible with the observational window of inflation. We analyze the implications of the theoretical uncertainty in the determination of the reheating temperature after inflation on the observable predictions of inflation and evaluate its impact on the degeneracy of the standard inflation consistency relation. We find that the detection of tensor perturbations and the theoretical uncertainties in the inflationary observable represents a significant challenge for the future Planck cosmic microwave background measurements: distinguishing between the observational signatures of the standard and braneworld single-field inflation scenarios. This work has been done in the frame of Planck Core Team activities.